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Marc Vrakking and Thomas Schultz: Attosecond and XUV Physics — 2013/10/28 — page I — le-tex

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Edited by

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Marc Vrakking

Attosecond and XUV Physics

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Marc Vrakking and Thomas Schultz: Attosecond and XUV Physics — 2013/10/28 — page II — le-tex

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Marc Vrakking and Thomas Schultz: Attosecond and XUV Physics — 2013/10/28 — page IV — le-tex

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Editors

Dr. Thomas Schultz

Max Born InstituteDiv. A: Attosecond PhysicsMax-Born-Strasse 212489 BerlinGermany

Dr. Marc Vrakking

Max Born InstituteMax-Born-Strasse 212489 BerlinGermany

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Printed in Singapore

Printed on acid-free paper

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Marc Vrakking and Thomas Schultz: Attosecond and XUV Physics — 2013/10/28 — page V — le-tex

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V

Contents

List of Contributors XIII

1 Attosecond and XUV Physics: Ultrafast Dynamics and Spectroscopy 1Marc Vrakking

1.1 Introduction 11.2 The Emergence of Attosecond Science 21.2.1 Attosecond Pulse Trains and Isolated Attosecond Pulses 31.2.2 Characterization of Attosecond Laser Pulses 41.2.3 Experimental Challenges in Attosecond Science 51.2.4 Attosecond Science as a Driver for Technological Developments 61.3 Applications of Attosecond Laser Pulses 71.4 Ultrafast Science Using XUV/X-ray Free Electron Lasers 91.5 The Interplay between Experiment and Theory 111.6 Conclusion and Outlook 12

References 13

Part One Laser Techniques 17

2 Ultrafast Laser Oscillators and Amplifiers 19Uwe Morgner

2.1 Introduction 192.2 Mode-Locking and Few-Cycle Pulse Generation 202.3 High-Energy Oscillators 232.4 Laser Amplifiers 25

References 29

3 Ultrashort Pulse Characterization 37Adam S. Wyatt

3.1 Motivation: Why Ultrafast Metrology? 373.1.1 Ultrafast Science: High-Speed Photography in the Extreme 383.2 Formal Description of Ultrashort Pulses 423.2.1 Sampling Theorem 453.2.2 Chronocyclic Representation of Ultrafast Pulses 463.2.3 Space-Time Coupling 463.2.4 Accuracy, Precision and Consistency 49

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VI Contents

3.3 Linear Filter Analysis 513.4 Ultrafast Metrology in the Visible to Infrared 533.4.1 Temporal Correlations 533.4.2 Spectrography 553.4.3 Sonography 603.4.4 Tomography 603.4.5 Interferometry 633.5 Ultrafast Metrology in the Extreme Ultraviolet 733.5.1 Complete Characterization of Ultrashort XUV Pulses

via Photoionization Spectroscopy 753.5.2 XUV Interferometry 813.6 Summary 85

References 85

4 Carrier Envelope Phase Stabilization 95Vincent Crozatier

4.1 Introduction 954.2 CEP Fundamentals 964.2.1 Time Domain Representation 964.2.2 Frequency Domain Representation 974.3 Stabilization Loop Fundamentals 994.3.1 The Noisy Source 994.3.2 Noise Detection 1004.3.3 Open-Loop Noise Analysis 1014.3.4 Feedback 1024.3.5 Closed-Loop Noise Analysis 1034.4 CEP in Oscillators 1044.4.1 Oscillators Peculiarities 1054.4.2 CEP Detection 1074.4.3 Actuation 1104.5 CEP in Amplifiers 1154.5.1 Amplifier Peculiarities 1164.5.2 CEP Detection 1194.5.3 Actuation 1234.5.4 Feedback Results 1244.5.5 Parametric Amplification 1264.6 Conclusion 129

References 129

5 Towards Tabletop X-Ray Lasers 135Philippe Zeitoun, Eduardo Oliva, Thi Thu Thuy Le, Stéphane Sebban,Marta Fajardo, David Ros, and Pedro Velarde

5.1 Context and Objectives 1355.2 Choice of Plasma-Based Soft X-Ray Amplifier 1375.2.1 Basic Aspects of High Harmonic Amplification 1385.2.2 Basic Aspects of Plasma Amplifiers 140

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Contents VII

5.3 2D Fluid Modeling and 3D Ray Trace 1415.3.1 ARWEN Code 1425.3.2 Model to Obtain 2D Maps of Atomic Data 1435.4 The Bloch–Maxwell Treatment 1495.5 Stretched Seed Amplification 1575.6 Conclusion 170

References 171

Part Two Theoretical Methods 177

6 Ionization in Strong Low-Frequency Fields 179Misha Ivanov

6.1 Preliminaries 1796.2 Speculative Thoughts 1796.3 Basic Formalism 1816.3.1 Hamiltonians and Gauges 1816.3.2 Formal Solutions 1826.4 The Strong-Field Approximation 1846.4.1 The Volkov Propagator and the Classical Connection 1856.4.2 Transition Amplitudes in the SFA 1866.5 Strong-Field Ionization: Exponential vs. Power Law 1896.5.1 The Saddle Point Approximation and the Classical Connection 1906.6 Semiclassical Picture of High Harmonic Generation 1956.7 Conclusion 198

References 199

7 Multielectron High Harmonic Generation: Simple Man on

a Complex Plane 201Olga Smirnova and Misha Ivanov

7.1 Introduction 2017.2 The Simple Man Model of High Harmonic Generation (HHG) 2037.3 Formal Approach for One-Electron Systems 2057.4 The Lewenstein Model: Saddle Point Equations for HHG 2097.5 Analysis of the Complex Trajectories 2147.6 Factorization of the HHG Dipole: Simple Man on a Complex Plane 2217.6.1 Factorization of the HHG Dipole in the Frequency Domain 2227.6.2 Factorization of the HHG Dipole in the Time Domain 2247.7 The Photoelectron Model of HHG: The Improved Simple Man 2277.8 The Multichannel Model of HHG: Tackling Multielectron Systems 2317.9 Outlook 2387.10 Appendix A: Supplementary Derivations 2417.11 Appendix B: The Saddle Point Method 2427.11.1 Integrals on the Real Axis 2437.11.2 Stationary Phase Method 2487.12 Appendix C: Treating the Cutoff Region: Regularization of Divergent

Stationary Phase Solutions 250

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VIII Contents

7.13 Appendix D: Finding Saddle Points for the Lewenstein Model 251References 253

8 Time-Dependent Schrödinger Equation 257Armin Scrinzi

8.1 Atoms and Molecules in Laser Fields 2588.2 Solving the TDSE 2598.2.1 Discretization of the TDSE 2608.2.2 Finite Elements 2638.2.3 Scaling with Laser Parameters 2658.3 Time Propagation 2668.3.1 Runge–Kutta Methods 2678.3.2 Krylov Subspace Methods 2688.3.3 Split-Step Methods 2698.4 Absorption of Outgoing Flux 2698.4.1 Absorption for a One-Dimensional TDSE 2708.5 Observables 2728.5.1 Ionization and Excitation 2728.5.2 Harmonic Response 2748.5.3 Photoelectron Spectra 2758.6 Two-Electron Systems 2788.6.1 Very Large-Scale Grid-Based Approaches 2788.6.2 Basis and Pseudospectral Approaches 2788.7 Few-Electron Systems 2828.7.1 MCTDHF: Multiconfiguration Time-Dependent Hartree–Fock 2838.7.2 Dynamical Multielectron Effects in High Harmonic Generation 2858.8 Nuclear Motion 287

References 290

9 Angular Distributions in Molecular Photoionization 293Robert R. Lucchese and Danielle Dowek

9.1 Introduction 2939.2 One-Photon Photoionization in the Molecular Frame 2979.3 Methods for Computing Cross-Sections 3029.4 Post-orientation MFPADs 3049.4.1 MFPADs for Linear Molecules in the Axial Recoil Approximation 3049.4.2 MFPADs for Nonlinear Molecules in the Axial Recoil Approximation 3069.4.3 Breakdown of the Axial Recoil Approximation Due to Rotation 3089.4.4 Breakdown of the Axial Recoil Approximation Due to Vibrational

Motion 3099.4.5 Electron Frame Photoelectron Angular Distributions 3099.5 MFPADs from Concurrent Orientation in Multiphoton Ionization 3109.6 Pre-orientation or Alignment, Impulsive Alignment 3149.7 Conclusions 315

References 315

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Contents IX

Part Three High Harmonic Generation and Attosecond Pulses 321

10 High-Order Harmonic Generation and Attosecond Light Pulses:

An Introduction 323Anne L’Huillier

10.1 Early Work, 1987–1993 32310.2 Three-Step Model, 1993–1994 32510.3 Trajectories and Phase Matching, 1995–2000 32810.4 Attosecond Pulses 2001 33110.5 Conclusion 332

References 335

11 Strong-Field Interactions at Long Wavelengths 339Manuel Kremer, Cosmin I. Blaga, Anthony D. DiChiara, Stephen B. Schoun,Pierre Agostini, and Louis F. DiMauro

11.1 Theoretical Background 34011.1.1 Keldysh Picture of Ionization in Strong Fields 34011.1.2 Classical Perspectives on Postionization Dynamics 34111.1.3 High-Harmonic Generation 34211.1.4 Wavelength Scaling of High-Harmonic Cutoff and Attochirp 34211.1.5 In-situ and RABBITT Technique 34411.2 Mid-IR Sources and Beamlines at OSU 34611.2.1 2-μm Source 34611.2.2 3.6-μm Source 34711.2.3 OSU Attosecond Beamline 34711.3 Strong-Field Ionization: The Single-Atom Response 34811.4 High-Harmonic Generation 35011.4.1 Harmonic Cutoff and Harmonic Yield 35011.4.2 Attochirp 35211.4.3 In-situ Phase Measurement 35211.4.4 RABBITT Method 35511.5 Conclusions and Future Perspectives 356

References 356

12 Attosecond Dynamics in Atoms 361Giuseppe Sansone, Francesca Calegari, Matteo Lucchini, and Mauro Nisoli

12.1 Introduction 36112.2 Single-Electron Atom: Hydrogen 36212.3 Two-Electron Atom: Helium 36512.3.1 Electronic Wave Packets 36612.3.2 Autoionization: Fano Profile 37112.3.3 Two-Photon Double Ionization 37312.4 Multielectron Systems 38012.4.1 Neon: Dynamics of Shake-Up States 38112.4.2 Neon: Delay in Photoemission 38412.4.3 Argon: Fano Resonance 386

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X Contents

12.4.4 Krypton: Auger Decay 38812.4.5 Krypton: Charge Oscillation 39012.4.6 Xenon: Cascaded Auger Decay 391

References 393

13 Application of Attosecond Pulses to Molecules 395Franck Lépine

13.1 Attosecond Dynamics in Molecules 39513.2 State-of-the-Art Experiments Using Attosecond Pulses 39713.2.1 Ion Spectroscopy 39813.2.2 Electron Spectroscopy 40213.2.3 Photo Absorption 40413.3 Theoretical Work 40513.3.1 Electron Dynamics in Small Molecules 40513.3.2 Electron Dynamics in Large Molecules 40613.4 Perspectives 41313.4.1 Molecular Alignment and Orientation 41313.4.2 Electron Delocalization between DNA Group Junction 41413.4.3 Similar Dynamics in Water and Ice 41613.4.4 More 41613.5 Conclusion 416

References 417

14 Attosecond Nanophysics 421Frederik Süßmann, Sarah L. Stebbings, Sergey Zherebtsov, Soo Hoon Chew,Mark I. Stockman, Eckart Rühl, Ulf Kleineberg, Thomas Fennel, andMatthias F. Kling

14.1 Introduction 42114.2 Attosecond Light-Field Control of Electron Emission and Acceleration

from Nanoparticles 42514.2.1 Imaging of the Electron Emission from Isolated Nanoparticles 42614.2.2 Microscopic Analysis of the Electron Emission 42914.3 Few-Cycle Pump-Probe Analysis of Cluster Plasmons 43314.3.1 Basics of Spectral Interferometry 43314.3.2 Oscillator Model Results for Excitation with Gaussian Pulses 43514.3.3 Spectral Interferometry Analysis of Plasmons in Small Sodium

Clusters 43714.4 Measurements of Plasmonic Fields with Attosecond Time

Resolution 43914.4.1 Attosecond Nanoplasmonic Streaking 43914.4.2 The Regimes of APS Spectroscopy 44114.4.3 APS Spectroscopy of Collective Electron Dynamics in Isolated

Nanoparticles 44214.4.4 Attosecond Nanoscope 44414.4.5 Experimental Implementation of the Attosecond Nanoscope 44614.5 Nanoplasmonic Field-Enhanced XUV Generation 449

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Contents XI

14.5.1 Tailoring of Nanoplasmonic Field Enhancement for HHG 45014.5.2 Generation of Single Attosecond XUV Pulses in Nano-HHG 45214.6 Conclusions and Outlook 454

References 455

Part Four Ultra Intense X-Ray Free Electron Laser Experiments 463

15 Strong-Field Interactions at EUV and X-Ray Wavelengths 465Artem Rudenko

15.1 Introduction 46515.2 Experimental Background 46715.2.1 What Is a “Strong” Field? 46715.2.2 Basic Parameters of Intense High-Frequency Radiation Sources 46915.2.3 Detection Systems 47115.3 Atoms and Molecules under Intense EUV Light 47315.3.1 Two-Photon Single Ionization of Helium 47315.3.2 Few-Photon Double Ionization of Helium and Neon 47615.3.3 Multiple Ionization of Atoms 48515.3.4 EUV-Induced Fragmentation of Simple Molecules 48715.4 EUV Pump–EUV Probe Experiments 49315.4.1 Split-and-Delay Arrangements and Characterization of the EUV

Pulses 49315.4.2 Nuclear Wave Packet Imaging in Diatomic Molecules 49515.4.3 Isomerization Dynamics of Acetylene Cations 49815.5 Experiments in the X-Ray Domain 49915.5.1 Multiple Ionization of Heavy Atoms: Role of Resonant Excitations 50015.5.2 Multiphoton Ionization of Molecules Containing High-Z Atoms 50615.6 Summary and Outlook 510

References 512

16 Ultraintense X-Ray Interactions at the Linac Coherent Light Source 529Linda Young

16.1 Introduction 52916.1.1 Comparison of Ultrafast, Ultraintense Optical, and X-Ray Lasers 53116.1.2 X-Ray Atom Interactions 53316.2 Atomic and Molecular Response to Ultraintense X-Ray Pulses 53616.2.1 Nonresonant High-Intensity X-Ray Phenomena 53716.2.2 Resonant High-Intensity X-Ray Phenomena 54016.3 Ultrafast X-Ray Probes of Dynamics 54316.4 Characterization of LCLS Pulses 54416.5 Outlook 546

References 549

17 Coherent Diffractive Imaging 557Willem Boutu, Betrand Carré, and Hamed Merdji

17.1 Introduction 55717.2 Far-Field Diffraction 559

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XII Contents

17.2.1 Optical Point of View 55917.2.2 Born Approximation 56117.2.3 Resolution 56217.2.4 Comments on the Approximations 56417.3 Source Requirements 56517.3.1 Coherence 56517.3.2 Signal-to-Noise Ratio 56817.3.3 Dose 56917.3.4 Different XUV Sources Comparison 57217.4 Solving the Phase Problem 57217.4.1 Oversampling Method 57217.4.2 Basics on Iterative Phasing Algorithms 57417.4.3 Implementations of Phase Retrieval Algorithms 57717.5 Holography 58317.5.1 Fourier Transform Holography 58317.5.2 HERALDO 58717.6 Conclusions 590

References 592

Index 599

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XIII

List of Contributors

Pierre AgostiniThe Ohio State UniversityDepartment of PhysicsColumbus, OH 43210USA

Roger BarlowUniversity of HuddersfieldHuddersfieldUnited Kingdom

Cosmin I. BlagaThe Ohio State UniversityDepartment of PhysicsColumbus, OH 43210USA

Willem BoutuCentre d’Etudes de SaclayAttophysics GroupUltrafast Coherent Imaging LabCEA-SPAM, Bât. 52291191 Gif-sur-YvetteFrance

Francesca CalegariDepartment of PhysicsPolitecnico di MilanoInstitute of Photonics andNanotechnologies, IFN-CNRPiazza L. da Vinci 3220133 MilanoItaly

Bertrand CarréCentre d’Etudes de SaclayAttophysics GroupCEA-SPAM, Bât. 52291191 Gif-sur-YvetteFrance

Soo Hoon ChewPhysik DepartmentLudwig-Maximilians-UniversitätMünchenAm Coulombwall 185748 GarchingGermany

Vincent CrozatierFASTLITECentre scientifique d’OrsayBât. 503Plateau du Moulon, BP 4591401 OrsayFrance

Anthony D. DiChiaraThe Ohio State UniversityDepartment of PhysicsColumbus, OH 43210USA

Louis F. DiMauroThe Ohio State UniversityDepartment of PhysicsColumbus, OH 43210USA